1. Ch 3 quiz follow-up The most missed problems had to do with the Pairwise Comparison method. This PowerPoint has a Pairwise Comparison question from the quiz worked out. A note about the midterm : You may use your past quizzes. You may NOT use your phone or your computer. If you want to use a calculator you will need to bring one to class.
2. Ch 3 quiz follow-up 2. Given the following information: <ul><ul><ul><li>b) Who wins if we use the pairwise comparison method? (might be a tie-show calculations) </li></ul></ul></ul>A B C 3 rd C A B 2 nd B C A 1 st 2 4 5 Ranking voters Number of
3. Ch 3 quiz follow-up 2. Given the following information: <ul><ul><ul><li>b) Who wins if we use the pairwise comparison method? (might be a tie-show calculations) </li></ul></ul></ul>Look at only A and B’s votes first. There will be a new table on the next slide with only A and B listed. A B C 3 rd C A B 2 nd B C A 1 st 2 4 5 Ranking voters Number of
4. Ch 3 quiz follow-up 2. Given the following information: <ul><ul><ul><li>b) Who wins if we use the pairwise comparison method? (might be a tie-show calculations) </li></ul></ul></ul>Look at only A and B’s votes first. Now the second column moves up so that A has 4-1st place votes and B has 4-2nd place votes. In the 3rd column A has 2-2nd place votes. There are no 3rd place votes since there are only 2 candidates. See next slide for a condensed table. A B 3 rd A B 2 nd B A 1 st 2 4 5 Ranking voters Number of
5. Ch 3 quiz follow-up 2. Given the following information: <ul><ul><ul><li>b) Who wins if we use the pairwise comparison method? (might be a tie-show calculations) </li></ul></ul></ul>Look at only A and B’s votes first. A B B 2 nd B A A 1 st 2 4 5 Ranking voters Number of
6. Ch 3 quiz follow-up 2. Given the following information: <ul><ul><ul><li>b) Who wins if we use the pairwise comparison method? (might be a tie-show calculations) </li></ul></ul></ul>Look at only A and B’s votes: A has 5 + 4 = 9 first place votes B has 2 first place votes So, in A vs. B, A wins. A B B 2 nd B A A 1 st 2 4 5 Ranking voters Number of
7. Ch 3 quiz follow-up 2. Given the following information: <ul><ul><ul><li>b) Who wins if we use the pairwise comparison method? (might be a tie-show calculations) </li></ul></ul></ul>Now look at only A and C’s votes. There will be a new table on the next slide with only A and C listed. A B C 3 rd C A B 2 nd B C A 1 st 2 4 5 Ranking voters Number of
8. Ch 3 quiz follow-up 2. Given the following information: <ul><ul><ul><li>b) Who wins if we use the pairwise comparison method? (might be a tie-show calculations) </li></ul></ul></ul>Now look at only A and C’s votes. Imagine (or re-draw a condensed table.) A has 5 first place votes C has 4+2 = 6 first place votes So in A vs. C, C wins . A C 3 rd C A 2 nd C A 1 st 2 4 5 Ranking voters Number of
9. Ch 3 quiz follow-up 2. Given the following information: <ul><ul><ul><li>b) Who wins if we use the pairwise comparison method? (might be a tie-show calculations) </li></ul></ul></ul>Look at only B and C’s votes first. There will be a new table on the next slide with only B and C listed. A B C 3 rd C A B 2 nd B C A 1 st 2 4 5 Ranking voters Number of
10. Ch 3 quiz follow-up 2. Given the following information: <ul><ul><ul><li>b) Who wins if we use the pairwise comparison method? (might be a tie-show calculations) </li></ul></ul></ul>Look at only B and C’s votes first. Imagine (or draw) a condensed table) B has 5 + 2 = 7 first place votes C has 4 first place votes So, in B vs. C, B wins . B C 3 rd C B 2 nd B C 1 st 2 4 5 Ranking voters Number of
11. Pairwise Comparison Method In this example: When A vs. B, A wins When A vs. C, C wins When B vs. C, B wins So, there was a tie. One of the three candidates (or players) would have to win 2 out of 3 head-to-head competitions to be a winner. The winner of the Pairwise Comparison method is also called the Condorcet candidate
12. Hope this example helps. Look over another in the textbook and try it out to see if you understand. We will work another example or two when we review for the midterm on June 24. Reminder: You may use your past quizzes during the midterm. You may NOT use your phone or your computer. If you want to use a calculator you will need to bring one to class.
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